Metrics Matter in Community Detection

Community detection is crucial in the analysis of social networks. Its main goal is to find groups of users densely connected among them, and sparsely connected between themselves. There are so many algorithms which makes it difficult for researchers to choose the best one for a specific dataset. In this paper, we provide a thorough comparison between five Community Detection (CD) algorithms- Girman-Newman (GN), Clauset-Newman-Moore (CNM), Label Propagation Algorithm (LPA), Louvain and Leiden. To evaluate in real social network datasets like Zachary's Karate Club, Dolphin networks and bigger ones such as Facebook, Twitter, LinkedIn along with citation networks we used different metrics modularity and NMI. We employed Normalized Mutual Information (NMI) to quantify the agreement of detected communities with their true ground-truth score and modularity for evaluating the overall quality of partitions given by diverse methods. Our experiments show that greedy and modularity-optimization algorithms are particularly well-suited. Notably, the Leiden algorithm had a better modularity value than Louvain (Q = 0.9141 and Q = 0.9051 of LinkedIn Network respectively) in most of the dataset. The NMI plot provided more explanation about Clauset-Newman-Moore (CNM), Louvain and Label Propagation Algorithm (LPA)which are in good agreement on community detection and their NMI score. These results would allow us to choose more rationally among the different community detection algorithms for social network analysis, by providing accurate quantitative benchmarks.

Community detection in graphs can be viewed as the estimation of a partition map that remains stable under admissible perturbations of graph topology and node attributes. While modern graph neural networks (GNNs) achieve strong empirical accuracy, they often exhibit severe assignment drift under minor perturbations, leading to illusory community structures. In this work, we propose DISPEL-GNN, a stability-aware graph learning framework that integrates spectral operator regularization, Bayesian uncertainty modeling, and risk-aware dynamic attention for perturbation-bounded community detection. The model explicitly constrains graph operators through uniform spectral norm bounds, high-frequency energy suppression, and commutator alignment while dynamically modulating message passing based on node-level spectral risk and epistemic uncertainty. We further formalize instability via assignment of drift functional and establish perturbation bounds linking drift to operator norms and spectral gaps, complemented by a PAC-Bayesian generalization guarantee. Extensive experiments on real-world benchmarks including Cora, Citeseer, Pubmed, Cora-Full, and DBLP demonstrate that DISPEL-GNN consistently reduces assignment drift by 18–35% under feature noise and edge perturbations while improving clustering quality with up to +3.0 NMI and +0.04 ARI compared to strong baselines such as GAT and Bayesian GNNs. The normalized mutual information (NMI), adjusted Rand index (ARI), and PAC-Bayesian (PAC) constraints serve as evaluative and theoretical instruments in this study. Additional studies on synthetic graphs with controlled spectral gaps confirm that the proposed method maintains stable community assignments in low-gap regimes where classical spectral and GNN-based methods degrade sharply. These results establish DISPEL-GNN as a mathematically grounded and practically effective framework for robust and interpretable community detection. A metric-wise dominance analysis shows that DISPEL-GNN achieves metric-wise dominance across most accuracy and robustness criteria, with minor tradeoffs in modularity on selected datasets. These results indicate that explicitly modeling stability and uncertainty provides a principled pathway toward reliable and interpretable community detection in noisy graph environments.

Community detection in complex networks plays a pivotal role in identifying the structural composition of nodes, enabling us to pinpoint key topological features critical for a multitude of applications.Usually, the complex networks are in graphical format in which graph nodes denote objects and edges denote a connection between two things.The existing techniques have limitations such as early convergence and local optima issues.To overcome this issue, this manuscript proposed an Improved Hybrid Harris Hawk and Coot Bird Optimization (IHHHCBO) algorithm in community detection.The optimum separate movement of CBO is incorporated in HHO population initialization to strengthen both optimizations.It is employed to initialize the population for enhancing the position of diversity and change with other individuals.The Karate, Dolphin, Football and Political Books datasets are considered for assessing the IHHHCBO performance.The Ensemble Mutation Strategy (EMS) is developed to produce mutant candidate locations which enhances the exploration and population diversity of optimization.The Normalized Mutual Information (NMI), and Modularity (Q) are considered fitness functions in this research.The IHHHCBO performance is estimated through metrics like NMI, Q, f1-score and accuracy.The IHHHCBO reaches better accuracy of 1, 1, 0.998 and 0.883 for Karate, Dolphin, Football and Political Books respectively which is better when compared to existing algorithms like Core Structure Extraction Algorithm (CSEA), and Modified Crossover Opposition-based Genetic Algorithm (MCOBGA).

A cascade information diffusion based label propagation algorithm for community detection in dynamic social networks

Community detection remains little explored in the analysis of biodiversity change. The challenges linked with global biodiversity change have also multiplied manifold in the past few decades. Moreover, most studies concerning biodiversity change lack the quantitative treatment central to species distribution modeling. Empirical analysis of species distribution and abundance is thus integral to the study of biodiversity loss and biodiversity alterations. Community detection is therefore expected to efficiently model the topological aspect of biodiversity change driven by land-use conversion and climate change; given that it has already proven superior for diverse problems in the domain of social network analysis and subgroup discovery in complex systems. Thus, quantum inspired community detection is proposed as a novel technique to predict biodiversity change considering tiger population in eighteen states of India; leading to benchmarking of two novel datasets. Elements of land-use conversion and climate change are explored to design these datasets viz.—Landscape based distribution and Number of tiger reserves based distribution respectively; for predicting regions expected to maximize Tiger population growth. Furthermore, validation of the proposed framework on the said datasets is performed using standard community detection metrics like—Modularity, Normalized Mutual Information (NMI), Adjusted Rand Index (ARI), Degree distribution, Degree centrality and Edge-betweenness centrality. Quantum inspired community detection has also been successful in demonstrating an association between biodiversity change, land-use conversion and climate change; validated statistically by Pearson’s correlation coefficient and p value test. Finally, modularity distribution based on parameter tuning establishes the superiority of the second dataset based on the number of Tiger reserves—in predicting regions maximizing Tiger population growth fostering species distribution and abundance; apart from scripting a stronger correlation of biodiversity change with land-use conversion.

Community structures are fundamental in understanding the structure and functionality of complex networks. Different optimization algorithms, including both single-objective and multi-objective approaches, have been employed to address the challenge of community detection. Recently, multi-objective evolutionary algorithms (MOEAs) have attracted many researchers to identify communities in static networks. Many algorithms have been proposed to find a solution that achieves a trade-off between exploring new areas of the solution space and improving the quality of existing solutions. In this trade-off is crucial; whereas exploitation improves existing solutions, it may fail to find better solutions from insufficiently explored regions of the solution space. Therefore, mutation in evolutionary algorithms greatly impacts community detection within social networks. Conventional mutation methods usually tend to apply too much randomness, which results in convergence being less precise about finding a suitable optimum solution. This paper introduces a new mutation called community strength enhancement (CSE) to enhance the search efficiency of the Multi-Objective Evolutionary Algorithm with Decomposition (MOEA/D) and speed up the convergence of the suggested algorithm. Moreover, the proposed algorithm overcomes the limitations of traditional MOEA/D by accurately and effectively identifying communities across a wide range of social networks. The enhanced algorithm was evaluated on two groups of datasets (twenty synthetic and four real-world) using normalized mutual information (NMI) and modularity (Q) across five baseline models. Integrating the CSE mutation strategy led to significant improvements in performance, particularly under high mixing parameters and in large-scale networks, as evidenced by increased NMI and modularity scores

Community detection is a fundamental task in network analysis in that it can express the characteristics of individual behaviors and the relationships between individuals in complex networks, thus revealing the functional and structural properties of various networks. However, as networks become larger and larger, how to quickly and accurately detect the community structure of large-scale networks has become a huge challenge nowadays. In this paper, an efficient algorithm, called Local Search for Community Detection (LSCD), is proposed to solve the multi-objective community detection problem. In the algorithm, an iterated local search is performed to search for non-dominated solutions in the solution space. To search for higher quality non-dominated solutions, this paper employs a learning-based strategy to select nodes in each round of the search. The strategy learns from the historical movement of the nodes and changes their selection probability according to their importance. Moreover, to search the entire solution space, this paper proposes a local search strategy that restricts one objective with a bound for a certain round, as well as an adaptive bound update mechanism. Experimental results on synthetic and real-world networks show that the proposed algorithm outperforms several state-of-the-art algorithms in terms of multi-objective optimization performance and accuracy in detecting the community structure of complex networks, since it performs best on 44 instances out of 46 in terms of Modularity (Q) and 29 out of 39 in terms of Normalized Mutual Information (NMI). In addition, the results show that the proposed algorithm has a good ability to handle large-scale networks.

Detecting Communities in networks is one of the appealing fields in computer science. A wide range of methods are proposed for this problem. These methods employ different strategies and optimization functions to detect communities (or clusters). Therefore, it seems a good idea to combine these strategies to take advantage of the strengths of the methods and overcome their problems. This is the idea behind consensus clustering technique which combines several clustering results into one. In this paper, we propose a very good-performing method based on consensus clustering to detect communities of a network. Our method, called “Azar”, employed several community detection methods as base methods. Then Azar generates a new compressed network based on the common views of the used base methods and, gives this new compressed network to the last community detection method to find the final partition. We evaluate our approach by employing real and artificial datasets. The implementation results compare the base methods with Azar according to accuracy measures such as modularity and Normalized Mutual Information (NMI). The results show the good-performing behavior of Azar even for the most difficult networks. The results show the brilliant power of Azar in comparison with all the other methods.

Community detection in complex networks remains a fundamental problem in network science, with wideranging applications from sociology to biology and recommendation systems.Building on recent advances in label diffusion techniques, we propose a novel hybrid approach-GraphSAGE-LBLD-that combines the structural awareness of the GraphSAGE embedding model with the local balance and speed advantages of the Label Balanced Label Diffusion (LBLD) algorithm.Our method integrates representation learning into the label propagation process, allowing for more semantically meaningful diffusion and improved stability across diverse network topologies.We empirically evaluate GraphSAGE-LBLD on multiple real-world SNAP datasets and benchmark against Louvain, classic Label Propagation, and the original LBLD.Results demonstrate that our model consistently achieves higher modularity and Normalized Mutual Information (NMI) scores, while maintaining comparable runtime.The integration of GraphSAGE enhances the representation of local neighbourhoods, resulting in finer community boundaries and better detection of small or overlapping clusters.Our method offers a practical, scalable, and more accurate alternative for modern community detection tasks.

Community detection is a kind of clustering task which aims to find groups of vertices densely connected internally but sparsely connected to other groups. In comparison with conventional clustering methods, community detection methods are able to examine structural, functional and dynamical properties of the networked data, beyond its physical attributes. However, such techniques have been barely explored in the literature as most of the machine learning data sets are represented as non-graph data (e.g., feature vectors, images, texts, and so on). In this work, we propose a simple community detection framework based on the literature that covers since the graph construction process from feature vectors generated from non-graph data until the application and evaluation of community detection methods over such a graph. The framework is further evaluated on the problem of invariant pattern clustering of images, which consists of given a set of image objects taken from different angles, positions or rotations, clustering the images related to each object. Experiments were conducted considering three community detection methods (fast greedy, walk-trap and label propagation) and two relevant clustering methods (k-means and HDBSCAN). The results indicate FG as the better choice among those algorithms as it usually approximates efficiently the ground-truth groups while also keeping a reasonable number of communities. Moreover, our results suggest that community detection may be an efficient task not only to cluster graph data, but also domain applications represented by non-graph data.

Community detection has gained significant research interest within the data mining field. It involves identifying subsets of nodes with dense internal connections and sparse external connections. Most studies on community detection focus solely on identifying non-overlapping communities in a static graph. However, in practice, communities often overlap, and the structure of the graphs is dynamically evolving. This dynamic nature leads to community changes and poses a significant challenge in detecting overlapping communities on temporal graphs (T-OCD). While graph neural networks have shown great performance in generating node representations for community detection, learning representations that capture temporal graph structures and support overlapping community detection remain an open question. To address these challenges, we present T-OCDIB , a novel approach for T emporal O verlapping C ommunity D etection guided by I nformation B ottleneck. Specifically, we first propose an overlapping community detection approach for static graphs, under the guidance of a community-oriented information bottleneck. This approach allows us to learn discriminative node representations specific to each community, facilitating the detection of overlapping communities. Following this, we extend this method to temporal graphs by presenting a temporal convolution module. This module uses adaptive weight matrices based on evolving graph structures to capture temporal dependencies for community detection. Additionally, to promote smooth transitions between consecutive communities, we introduce a temporal smoothing module to further constrain changes in community structure. We evaluate the proposed approach on both real-world and synthetic temporal networks. Experimental results illustrate the superiority of T-OCDIB over other community detection methods.

The community structure is a major feature of bipartite networks, which serve as a typical model for empirical networks consisting of two kinds of nodes. Over the past years, community detection has drawn a lot of attention. Numerous methods for community detection have been put forth. Nevertheless, some of them need a lot of time, which restricts their use in large networks. While several low-time complexity algorithms exist, their practical value in real-world applications is limited since they are typically non-deterministic. Typically, in bipartite networks, a unipartite projection of one part of the network is created, and then communities are detected inside that projection using methods for unipartite networks. Unipartite projections may yield incorrect or erroneous findings as they inevitably include a loss of information. In this paper, BiVoting, a two-mode and deterministic community detection method in bipartite networks, is proposed. This method is a consequence of bipartite modularity, which quantifies the strength of partitions and is based on how people vote in social elections. The proposed method’s performance was evaluated, and comparison with four common community detection methods in bipartite networks shows that for calculating the modularity score in large networks, BiVoting performs better than the best method.

Multi-relational community detection is a very important task in social network analysis because in the real world social networks are mostly multi-relational. In this paper, we propose a user-dependent method to detect communities in multi-relational social networks. We define a multi-relational community as a shared community over multiple single-relational graphs while the quality of a partitioning of nodes is assessed by a multi-relational modularity, and we design a desirable set of communities to represent the requests of users and use Normalized mutual information (NMI) between the desirable set of communities and the sets of communities detected in each single-relational graph as the weights for measuring the importance of all kinds of relationship types. We then use a greedy agglomerative manner to identify communities. Experiments have been conducted on synthetic networks to evaluate the effectiveness of the proposed approach.

Firstly, this paper selects multiple urban agglomerations to construct the network relationship of urban agglomerations from the three dimensions of transportation, economy and information. Secondly, it uses the community detection called Louvain algorithm to detect the community structure, focusing on the internal and external research of the community structure and based on NMI (Normalized Mutual Information) index for analysis and comparison. The results show that some cities have special positioning, which have different development space in the same types of network or different types of networks. For example, Hefei mainly play the role of high-speed rail collection and distribution within the urban agglomeration, and mainly play the role of high-speed distribution externally, while other cities such as Qianjiang do the opposite. Cities such as Yueyang are closely related to inner cities in the transportation dimension, but they are closely related to the outer cities in the economic or information dimension. Secondly, spatial distance has an impact on the phenomenon of community structure. Although spatial distance is not the sole factor influencing the closeness of urban agglomerations, it can be combined with the positioning of the urban agglomeration and the actual development situation to affect the phenomenon of the community structure. Thirdly, based on the comparison with the NMI analysis of the national policy urban agglomeration community structure, it is found that transportation not only promotes the development of the regional economy, but also promotes the formation of urban agglomerations. The community detection results from the perspective of the traffic dimension and the national policy urban agglomeration classification Relatively most consistent.KeywordsUrban trafficCommunity structureLouvain algorithmNMI

As dynamic systems, social networks exhibit continuous topological changes over time, and are typically modeled as temporal networks. In order to understand their dynamic characteristics, it is essential to investigate temporal community detection (TCD), which poses significant challenges compared to static network analysis. These challenges arise from the need to simultaneously detect community structures and track their evolutionary behaviors. To address these issues, we propose TCDA-NE, a novel TCD algorithm that combines evolutionary clustering with convex non-negative matrix factorization (Convex-NMF). Our method innovatively integrates community structure into network embedding, preserving both microscopic details and community-level information in node representations while effectively capturing the evolutionary dynamics of networks. A distinctive feature of TCDA-NE is its utilization of a common-neighbor similarity matrix, which significantly enhances the algorithm’s ability to identify meaningful community structures in temporal networks. By establishing coherent relationships between node representations and community structures, we optimize both the Convex-NMF-based representation learning model and the evolutionary clustering-based TCD model within a unified framework. We derive the updating rules and provide rigorous theoretical proofs for the algorithm’s validity and convergence. Extensive experiments on synthetic and real-world social networks, including email and phone call networks, demonstrate the superior performance of our model in community detection and tracking temporal network evolution. Notably, TCDA-NE achieves a maximum improvement of up to 0.1 in the normalized mutual information (NMI) index compared to state-of-the-art methods, highlighting its effectiveness in temporal community detection.